基于Hoek-Brown准则的应变软化模型有限元数值实现研究

研究提出一种Hoek-Brown（H-B）准则应变软化模型的有限元数值实现方法。分析当前不同脆塑性计算方法的合理性，发现塑性位势跌落可正确计算岩石不同类型破坏，而偏应力等比例跌落和最小主应力不变跌落均存在不足。在此基础上，推导写出基于塑性位势跌落的H-B准则脆塑性隐式本构积分算法，及H-B准则理想弹塑性隐式本构积分算法，并采用一系列应力跌落-塑性流动，将H-B准则应变软化模型嵌入有限元软件ABAQUS中。比较应变软化圆隧围岩收敛位移及应力分布的解析解与本文有限元解，发现二者吻合良好，验证了所建H-B准则应变软化模型的正确性。对某薄上覆盖岩层高内水压输水隧洞工程的计算结果表明，相较理想弹塑性模型，所建应变软化模型可正确反映隧洞顶部围岩塑性区贯通引起的整体结构失稳破坏现象，为工程选择衬砌方案提供依据。

A FINITE ELEMENT IMPLEMENTATION OF THE STRAIN-SOFTENING MODEL BASED ON THE HOEK-BROWN CRITERION

A finite element method to model the Hoek-Brown(H-B)criterion with the strain-softening behavior is presented.Firstly,the reasonability of the current brittle-plastic calculation methods is analyzed.It is found that the plastic potential theory based on the Il’yushin’s postulation can correctly capture different types of rock failure,while the methods based on the deviator stress dropping or the constant minor principal stress in the brittle-plastic process both have shortcomings.Then,with respect to the H-B criterion,the brittle-plastic implicit constitutive integration algorithm based on the plastic potential theory is deduced,while the elastic-perfectly plastic implicit constitutive integration algorithm is also presented.With a series of stress dropping and perfectly plastic flow,the strain-softening model is embedded in the program ABAQUS.It is validated by comparing the finite element calculations of the displacement curve and the stress distribution in the surrounding rock mass with strain-softening behavior of a circular tunnel with analytical solutions,showing good agreement between them.Finally,the calculation results of a diversion tunnel with thin rock overburden under high internal water pressure show that the proposed model has great advantages over the elastic-perfectly plastic model in predicting the instability failure caused by plastic run-through on the top of the tunnel,providing a reference for further lining design.